When snow melts on concrete faster than it melts on grass it's because the concrete is warmer and the snow becomes warmer due the ground temperature.
So the snow melts faster on the concrete as a result of the snow being closer to the ground.
Also if the sun is shining on the concrete the sun heats up the concrete better than it does the grass so that's another reason that snow melts faster on concrete than it does on grass.
When the snow is on grass the grass blades actually hold the snow up above the ground so that the snow doesn't get warmed up as good and fast as it would if it were in contact with the ground directly.
Also sometimes you might actually see some leftover snow on concrete and it be melted off the grass.